Hyper-redundant snakelike serial robots are of great interest due to their application in search and rescue during disaster relief in highly cluttered environments and recently in the field of medical robotics. A key feature of these robots is the presence of a large number of redundant actuated joints and the associated well-known challenge of motion planning. This problem is even more acute in the presence of obstacles. Obstacle avoidance for point bodies, nonredundant serial robots with a few links and joints, and wheeled mobile robots has been extensively studied, and several mature implementations are available. However, obstacle avoidance for hyper-redundant snakelike robots and other extended articulated bodies is less studied and is still evolving. This paper presents a novel optimization algorithm, derived using calculus of variation, for the motion planning of a hyper-redundant robot where the motion of one end (head) is an arbitrary desired path. The algorithm computes the motion of all the joints in the hyper-redundant robot in a way such that all its links avoid all obstacles present in the environment. The algorithm is purely geometric in nature, and it is shown that the motion in free space and in the vicinity of obstacles appears to be more natural. The paper presents the general theoretical development and numerical simulations results. It also presents validating results from experiments with a 12-degree-of-freedom (DOF) planar hyper-redundant robot moving in a known obstacle field.